Question

The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (source: american dietetic association). if a sample of 50 individuals is randomly selected, find the probability that the mean of the sample will be less than 200 pounds.

Answer 1

Given:
Mean, μ = 196
Std. dev., σ = 22
A sample size of 50 (> 30) is large enough to provide meaningful data.

The random variable is x = 200.
The z-score is
z = (x - μ)/σ = (200 - 196)/22 = 0.1818

From normal distribution tables, obtain
Prob(X < 200) = 0.572 = 57.2%

Answer: 57.2%